Question

Periksa Kebenaran kesamaan berikut!
1. (Sec t - 1) (Sec t + 1) = tan2 t
2. Sec t - Sin t tan t = Cos t
3. (1 - Cos2 x) (1 + Cot2 x) = 1

Answer 1

(sec t - 1)(sec t + 1) = sec²t - 1 = 1/cos²t - 1 = (1 - cos² t)/cos²t = sin²t/cos²t = tan²t

sec t - sin t tan t = 1/cos t - sin t . sin t/cos t = 1/cos t - sin²t/cos t = (1-sin²t)/cos t = cos²t/cos t = cos t

(1-cos²x)(1+cot²x) = sin²x. cosec²x = sin²x . 1/sin²x = 1